Уолтер Тевис: The Ifth of Oofth

Farnsworth had to go meddle in a muddle and the results . . . well, just wait and see!　

Farnsworth had invented a new drink that night. He called it a mulled sloe gin toddy. Exactly as fantastic as it sounds—ramming a redhot poker into a mugful of warm red gin, cinnamon, cloves and sugar, and then drinking the fool thing—but like many of Farnsworth’s ideas, it managed somehow to work out. In fact, its flavor had become completely acceptable to me after the third one.　

When he finally set the end of his steaming poker back on the coals for rest and regeneration, I leaned back warmly in my big leather chair—the one he had rigged up so that it would gently rock you to sleep if you pressed the right button—and said, “Oliver, your ingenuity is matched only by your hospitality.”　

Farnsworth blushed and smiled.　

He is a small, chubby man and blushes easily. “Thank you,” he said. “I have another new one. I call it a jelled vodka fizz —you eat it with a spoon. You may want to try it later. It’s — well — exceptional.”　

I suppressed a shudder at the thought of eating jelled vodka and said, “Interesting, very interesting,” and since he didn’t reply, we both stared at the fire for a while, letting the gin continue its　pleasant work. Farnsworth’s bachelor’s home was very comfortable and relaxing, and I always en joyed my Wednesday night visits there thoroughly. I suppose most men have a deep-seated love for open fires and liquor—however fantastically prepared — and deep, comfortable leather armchairs.　

Then, after several minutes, Farnsworth abruptly bounced to his feet and said, “There’s a thing I wanted to show you. Made it last week. Didn’t pull it off too well, though.”　

“Really?” I said I'd thought the drinks had been his usual weekly brainchild. They seemed quite enough.　

“Yes,” he said, trotting over to the door of the study. “It’s downstairs in the shop. Ill get it.” And he bounced out of the room, the paneled door closing as it had opened, automatically, behind him.　

I TURNED back to the fire again, pleased that he had made something in the machine shop—the carpentry shop was in a shed in the backyard; the chemistry and optical labs in the attic—for he was his most proficient with his lathe and milling machines. His self-setting, variable-twist thumb bolt had been a beautiful piece of work and its patent had netted him, as had several other machined devices, a remarkable sum.　

He returned in a minute, carrying a very odd-looking thing with him, and set it on the table beside my chair. I examined it silently for a minute while Farnsworth stood over me, half-smiling, his little green eyes wide, sparkling in the reflected, flickering light from the fire. I knew he was suppressing his eagerness for my comment, but I was uncertain what to say.　

The thing, upon examination, appeared simple: a more or less cross-shaped construction of several dozen one-inch cubes, half of them of thin, transparent plastic, the other half made of thin　little sheets of aluminum. Each cube seemed to be hinged to two others very cunningly and the arrangement of them all was somewhat confusing.　

Finally, I said, “How many cubes?” I had tried to count them, but kept getting lost.　

“Sixty-four” he said. “I think.” “You think?”　

“Well—” He seemed embarrassed. “At least I made sixty-four cubes, thirty-two of each kind; but somehow I haven’t been able to count them since. They seem to . . . get lost, or shift around, or something.”　

“Oh?” I was becoming interested. “May I pick it up?”　

“Certainly,” he said, and I took the affair, which was surprisingly lightweight, in my hands and began folding the cubes around on their hinges. I noticed then that some were open on one side and that certain others would fit into these if their hinging arrangements would allow them to.　

I began folding them absently and said, “You could count them by marking them one at a time. With a crayon, for instance.”　

“As a matter of fact,” he admitted, blushing again, “I tried that. Didn’t seem to work out.　When I finished, I found I had marked six cubes with the number one and on none of them could I find, a two or three, although there were two fours, one of them written in reverse and in green.” He hesitated. “I had used a red marking pencil.” I saw him shudder slightly as he said it, although his voice had been casual-sounding enough. “I rubbed the numbers off with a　damp cloth and didn’t . . . try it again.”　

“Well,” I said. And then, “What do you call it?”　

“A pentaract.”　

НE SAT back down again in his armchair. “Of course, that name really isn’t accurate. I suppose a pentaract should really be a four-dimensional pentagon, and this is meant to be a picture of a five-dimensional cube.”　

“A picture ?” It didn’t look like a picture to me.　

“Well, it couldn’t really have five dimensionality — length, width, breadth, ifth and oofth — or I don’t think it could.” His voice faltered a little at that. “But it’s supposed to illustrate what you might call the layout of an object that did have those.” “What kind of object would that be?” I looked back at the thing in my lap and was mildly surprised to see that I had folded a good many of the cubes together.　

“Suppose,” he said, “you put a lot of points in a row, touching; you have a line—a one-dimensional figure. Put four lines together at right angles and on a plane; a square—two-dimensional. Six squares at right angles and extended into real space give you a cube—three dimensions. And eight cubes extended into four physical dimensions give you a tesseract, as it’s called—”

“And eight tesseracts make a pentaract,” I said. “Five dimensions.”　

“Exactly. But naturally this is just a picture of a pentaract, in that sense. There probably isn’t any ifth and oofth at all.”　

“I still don’t know what you mean by a picture," I said, pushing the cubes around interestedly.　

“You don’t?” he asked, pursing his lips. “It’s rather awkward to explain, but. ... well, on the surface of a piece of paper, you can make a very realistic picture of a cube—you know, with perspective and shading and all that kind of thing—and what you’d actually be doing would be illustrating a three-dimensional object, the cube, by using only two dimensions to do it with.”　

“And of course,” I said, “you could fold the paper into a cube. Then you’d have a real cube.”

He nodded. “But you’d have to use the third dimension—by folding the flat paper up —to do it. So, unless I could fold my cubes up through ifth or oofth, my pentaract will have to be just a poor picture. Or, really, eight pictures. Eight tessеracts, pictures of four-dimensional objects, stuck together to make a picture of five dimensions.”　

“Well!” I said, a bit lost. “And what do you plan to use it for?”

“Just curiosity.” And then,　abruptly, looking at me now, his eyes grew wide and he bumped up out of his chair. He said breathlessly, ‘What have you done to it?”　

I looked down at my hands. I was holding a little structure of eight cubes, joined together in a small cross. “Why, nothing,” I said, feeling a little foolish. “I only folded most of them together.”　

“That’s impossible! There were only twelve open ones to begin with! All of the others were six-sided!”　

FARNSWORTH made a grab for it, apparently beside himself, and the gesture was so sudden that I drew back. It made Farnsworth miss his grab and the little object flew from my hands and hit the floor, solidly, on one of its comers. There was a slight bump as it hit, and a faint clicking noise, and the thing seemed to crumple in a very peculiar　way. And sitting in front of us on the floor was one little one-inch cube, and nothing else.